Question:
If $$\cos 25^\circ + \sin 25^\circ = k,$$ then what is $\cos 20^\circ$?
What I did:
I tried to square both sides, and obtained that $\sin 50 = k^2 -1$, however, this didn't get me anywhere. Then I tried splitting 25 into 20 + 5 but that didn't get me anywhere either. Can someone just point me in the right direction?
Best Answer
Hint
Take into account that $20 = 45 -25$. Develop $\displaystyle\cos(45^\circ-25^\circ)$ and remember that $\displaystyle\cos(45^\circ)=\sin(45^\circ)=\frac{\sqrt 2}2$ and see what happens.
I am sure that you can take from here.